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An upward open parabola passes through 5 plotted points on a coordinate plane with x-axis ranging from negative 12 to 12 in increments of 2 and y-axis ranging from negative 6 to 18 in increments of 2.

Interpret the key features of the graph. What type of transformation occurred from the parent function?

(1 point)
Responses

This is a vertical stretch of the parent function y=x2
due to the changes in the y-intercept.
This is a vertical stretch of the parent function y equals x squared due to the changes in the y -intercept.

This is a vertical stretch of the parent function y=x2
due to the changes in the x-intercept.
This is a vertical stretch of the parent function y equals x squared due to the changes in the x- intercept.

This is a vertical stretch of the parent function y=x2
due to the changes in the x-coordinates of each point.
This is a vertical stretch of the parent function y equals x squared due to the changes in the x -coordinates of each point.

This is a vertical stretch of the parent function y=x2
due to the changes in the y-coordinates of each point.

1 answer

Based on the description provided, the parabola passes through five plotted points and shows characteristics that differ from the parent function \(y = x^2\). Generally, we interpret transformations based on the changes in the graph's shape and position in relation to key features such as the vertex and intercepts.

In this case, the mention of vertical stretch suggests that the parabola is narrower than the parent function, which is typically the case when points on the graph are farther from the x-axis compared to the points of the parent function.

The appropriate interpretation of the transformation would most likely be:

This is a vertical stretch of the parent function \(y = x^2\) due to the changes in the y-coordinates of each point.

This response accurately highlights that the upward opening of the parabola and its proximity to the y-axis indicate a vertical stretch, affecting the y-coordinates of the points in relation to the standard parabola.